Erdos and Rényi Conjecture

Saharon Shelah

doi:10.1006/jcta.1997.2845

Erdos and Rényi Conjecture

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

Affirming a conjecture of Erdos and Rényi we prove that for any (real number)c₁>0 for some c₂>0, if a graph G has no c₁(log n) nodes on which the graph is complete or edgeless (i.e.,G exemplifies G(c₁log n)²₂), then G has at least 2^c2nnon-isomorphic (induced) subgraphs.

Original language	English
Pages (from-to)	179-185
Number of pages	7
Journal	Journal of Combinatorial Theory. Series A
Volume	82
Issue number	2
DOIs	https://doi.org/10.1006/jcta.1997.2845
State	Published - May 1998

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title = "Erdos and R{\'e}nyi Conjecture",

abstract = "Affirming a conjecture of Erdos and R{\'e}nyi we prove that for any (real number)c1>0 for some c2>0, if a graph G has no c1(log n) nodes on which the graph is complete or edgeless (i.e.,G exemplifies G(c1log n)22), then G has at least 2c2nnon-isomorphic (induced) subgraphs.",

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AB - Affirming a conjecture of Erdos and Rényi we prove that for any (real number)c1>0 for some c2>0, if a graph G has no c1(log n) nodes on which the graph is complete or edgeless (i.e.,G exemplifies G(c1log n)22), then G has at least 2c2nnon-isomorphic (induced) subgraphs.

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Erdos and Rényi Conjecture

Abstract

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